1. Use the Concept of slope to find t such that the three points are collinear.
1)(1,-4),(t,3),(5,10)

2. Find an equation of the line that passes through the given point and has the specified slope, and find three additional points through which the line passes.

3. Determine the x and y intercepts of the graph of the equation algebraically.
-x+y=3

Solution Preview

1) If the points are collinear, the slope of the line joining any two points must be same.
So, we calculate the slope of line joining the points (1, -4) and (5, 10) which is given by
[10-(-4)]/(5-1)=14/4=7/2
so it must be same with the line ...

... We have . Besides, . Hence . From we obtain . Therefore . (1) Similarly to ii), it is sufficient to find any non-collinear points on the plane (1). Such points...

... the point (6,0,-2) and contains the line x = 4 - 2t, y = 3 + 5t, z = 7 + 4t. We define a plane by a vector N which is perpendicular to any vector collinear...

... If the system results c=0, then which implies the slopes of the line joining any two pairs of the points are same ie., the points are collinear. ...

... Find a vector with the following three characteristics: initial point at the origin, collinear but in the opposite direction of vector AB , length 3. ...

... Since A,B and C are collinear, with B between A and C, we may assume C*B*A uuu r If C*B*A and l is the line through B,A, and C, then for every point P lying on ...

... 9. Since C is colinear with A and G, square BAGF must be twice in ... Century, Euclidean geometry was usually understood to be the study of points, lines, angles ...

... is looking for the intersection of the angle and line, which would be points F and B 2) Vertical angles are congruent, so angle 4 is 120. Collinear angles are ...